enum cv::NormTypes

Overview

norm types

  • For one array:
#include <base.hpp>

enum NormTypes
{
    NORM_INF       = 1,
    NORM_L1        = 2,
    NORM_L2        = 4,
    NORM_L2SQR     = 5,
    NORM_HAMMING   = 6,
    NORM_HAMMING2  = 7,
    NORM_TYPE_MASK = 7,
    NORM_RELATIVE  = 8,
    NORM_MINMAX    = 32,
};

Detailed Documentation

norm types

  • For one array:

    \[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } { \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } { \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\]

  • Absolute norm for two arrays

    \[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } { \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } { \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\]

  • Relative norm for two arrays

    \[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE_INF}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L1}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L2}\) }\]

As example for one array consider the function \(r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\). The \(L_{1}, L_{2}\) and \(L_{\infty}\) norm for the sample value \(r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\) is calculated as follows

\[\begin{split}\begin{align*} \| r(-1) \|_{L_1} &= |-1| + |2| = 3 \\ \| r(-1) \|_{L_2} &= \sqrt{(-1)^{2} + (2)^{2}} = \sqrt{5} \\ \| r(-1) \|_{L_\infty} &= \max(|-1|,|2|) = 2 \end{align*}\end{split}\]

and for \(r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\) the calculation is

\[\begin{split}\begin{align*} \| r(0.5) \|_{L_1} &= |0.5| + |0.5| = 1 \\ \| r(0.5) \|_{L_2} &= \sqrt{(0.5)^{2} + (0.5)^{2}} = \sqrt{0.5} \\ \| r(0.5) \|_{L_\infty} &= \max(|0.5|,|0.5|) = 0.5. \end{align*}\end{split}\]

The following graphic shows all values for the three norm functions \(\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\) and \(\| r(x) \|_{L_\infty}\). It is notable that the \(L_{1}\) norm forms the upper and the \(L_{\infty}\) norm forms the lower border for the example function \(r(x)\).

Graphs for the different norm functions from the above example

Enum Values

NORM_RELATIVE

flag

NORM_MINMAX

flag